Errors compensation caused by time delay of digital sensors

The paper is devoted to improving the accuracy of digital sensors with a time lag. The relevance of the topic is due to the widespread use of sensors of this type, which is largely due to a sharp increase in the requirements for measurement accuracy. The timeliness is associated also with the extensive application of digital technologies for information processing in control systems, communications, monitoring and many others. To eliminate the errors caused by the time delay of digital sensors, it is suggested to use an astatic high-speed corrector. The applicability of this corrector is justified by the properties of discrete-time dynamical systems. In this regard, at first, the conditions are considered under which the discrete systems are physically realizable and have a finite duration of the transient since in this latter case they are the fastest. It is also shown that in order to measure a polynomial signal of limited intensity with zero error in steady-state mode, the astatism order of the sensor must be one value greater than the degree of this signal. Based on the above conditions, the main result of the article is proved – a theorem in which the conditions for the existence of the astatic high-speed corrector are established. When this corrector is switched on at the output of the digital sensor or when its software is being corrected an upgraded sensor is formed, the error of which will be zero in steady-state mode. This is due to the fact that the corrector eliminates the error of the digital sensor caused by its time delay, which is assumed to be multiple of the sampling period. The order of the corrector as a system is determined by the integer solution of the equation obtained in the work, which relates the degree of the measured polynomial signal, the time delay of the digital sensor, the permissible overshoot of the upgraded sensor and the relative order of the desired corrector. This equation is solved for the cases, where the degree of the measured signals is not greater than one, the overshoot is equal to the frequently assigned values, and the time delay does not exceed four sampling periods. The corresponding order of the upgraded sensor is given in tabular form. This makes it possible to find the required corrector without solving the shown equation in many cases. The effectiveness of the suggested approach with respect to improving the accuracy of digital sensors is shown by a numerical example. The zero error value of the upgraded sensor is confirmed both by computer simulation and numerical calculation. The results obtained can be used in the development of high-precision digital sensors of various physical quantities.